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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d828ae1c",
   "metadata": {},
   "source": [
    "# FIR Filter Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9aed9f51",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "from numpy.fft import fft,ifft,fftshift\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9a16a6d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Anfangs werte noch variabel machen \n",
    "delays = [3,5,2]\n",
    "ampl = [0.2,0.5,0.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ad0edf9",
   "metadata": {},
   "source": [
    "# Dealy Window\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bf92d73a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d =0\n",
    "k = np.linspace(-5,10,1000)\n",
    "h_ideal = np.sinc(k-d)\n",
    "plt.plot(k,h_ideal)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dd93e444",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 4.5\n",
    "window_sample= np.arange(np.round(d-(n-1)/2),np.round(d+(n+1)/2))\n",
    "window = []\n",
    "for ws in window_sample:  \n",
    "    idx = (np.abs(k-ws)).argmin()\n",
    "    window.append(idx)\n",
    "    \n",
    "plt.plot(k,h_ideal)\n",
    "plt.plot(window_sample,h_ideal[window],\"-*\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b0c2d2",
   "metadata": {},
   "source": [
    "# FIR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "efc93b69",
   "metadata": {},
   "outputs": [],
   "source": [
    "delay = 3\n",
    "amplitude = 1\n",
    "\n",
    "d_int = int(np.floor(delay))\n",
    "#d_frac = delay - d_int\n",
    "\n",
    "h_int = np.concatenate([np.zeros(d_int-1), [amplitude], np.zeros(3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43372541",
   "metadata": {},
   "outputs": [],
   "source": [
    "#H_int = fft(h_int)\n",
    "#h = ifft(H_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a32cb580",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.random.randint(0, 10, size = 20)# Signal\n",
    "\n",
    "y = np.convolve(test.real, h_int)#Faltung\n",
    "\n",
    "plt.stem(test, linefmt=\"C0-\")\n",
    "plt.stem(y, linefmt='C1-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "39fb3489",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 9, 7, 5, 7, 9, 0, 5, 5, 7, 5, 1, 0, 8, 6, 9, 0])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7fd06347",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 0., 0., 0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_int"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a9612999",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 9., 8., 7., 6., 9., 7., 5., 7., 9., 0., 5., 5., 7., 5., 1.,\n",
       "       0., 8., 6., 9., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "706a51b1",
   "metadata": {},
   "source": [
    "# FIR mit Delay \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "79e18131",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tap with amplitude=1, delay=5.2\n",
      "Creating filter of order N=11.0\n",
      "[ 1.          0.04454711 -0.05846808  0.08504448 -0.15591488  0.93548928\n",
      "  0.23387232 -0.10394325  0.06682066 -0.04923628  0.03897872 -0.03225825]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "delay = 5.2\n",
    "ampl = 1\n",
    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
    "    \n",
    "order = 2 * np.floor(delay) + 1 #N\n",
    "print(f\"Creating filter of order N={order}\")\n",
    "\n",
    "skip = np.floor(delay) - (order - 1) / 2 #M\n",
    "assert skip >= 0\n",
    "\n",
    "samples = np.arange(0, order+1)\n",
    "\n",
    "h = ampl*(np.sinc(samples-delay)) #sinc\n",
    "\n",
    "h[0] = 1\n",
    "\n",
    "print(h)\n",
    "\n",
    "plt.stem(samples, h)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c89c83ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f3e0dc80c40>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(200)\n",
    "\n",
    "signal = np.sin(2 * np.pi * t * 0.05)\n",
    "\n",
    "signal_shifted = np.convolve(h, signal, mode='full')\n",
    "\n",
    "plt.plot(t, signal)\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "plt.plot(signal_shifted)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d51d8a62",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tap with amplitude=[4, 1], delay=[5, 6.2]\n",
      "14\n",
      "[ 1.55926873e-16 -1.55926873e-16  1.55926873e-16 -1.55926873e-16\n",
      "  1.55926873e-16  4.00000000e+00  1.55926873e-16 -1.55926873e-16\n",
      "  1.55926873e-16 -1.55926873e-16  1.55926873e-16 -1.55926873e-16\n",
      "  0.00000000e+00  0.00000000e+00]\n",
      "[ 0.03017707 -0.03598036  0.04454711 -0.05846808  0.08504448 -0.15591488\n",
      "  0.93548928  0.23387232 -0.10394325  0.06682066 -0.04923628  0.03897872\n",
      " -0.03225825  0.02751439]\n",
      "[ 1.         -0.03598036  0.04454711 -0.05846808  0.08504448  3.84408512\n",
      "  0.93548928  0.23387232 -0.10394325  0.06682066 -0.04923628  0.03897872\n",
      " -0.03225825  0.02751439]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "delay = [5,6.2]\n",
    "ampl = [4,1]\n",
    "print(f\"Tap with amplitude={ampl}, delay={delay}\")\n",
    "\n",
    "max_order = 2 * np.floor(np.max(delay)) + 1\n",
    "max_samples = np.arange(0, max_order +1) \n",
    "max_len = len(max_samples)\n",
    "print(max_len)\n",
    "\n",
    "sum_x = np.zeros(int(max_len))\n",
    "\n",
    "for (a,d) in zip(ampl,delay):\n",
    "    \n",
    "    order = 2 * np.floor(d) + 1\n",
    "    \n",
    "    skip = np.floor(d) - (order - 1) / 2 #M sollte immer 0 sein \n",
    "    assert skip >= 0\n",
    "\n",
    "    samples = np.arange(0, order+1 ) \n",
    "\n",
    "    h = a*(np.sinc(samples-d)) #sinc\n",
    "    h_len = np.concatenate([h, np.zeros(max_len-len(h))])\n",
    "    print(h_len)\n",
    "    sum_x += h_len\n",
    "    \n",
    "\n",
    "sum_x[0] = 1\n",
    "print(sum_x)\n",
    "\n",
    "\n",
    "\n",
    "plt.stem(max_samples, sum_x)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "81b4ff57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delay = [5,6]\n",
    "np.max(delay)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "330915ff",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}